(A) point $P$ lying on the line segment $\overline{AB}$ divides the segment into two parts: $AP$ and $PB$.By definition,the division ratio of a line s

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(A) point $P$ lying on the line segment $\overline{AB}$ divides the segment into two parts: $AP$ and $PB$.By definition,the division ratio of a line segment $\overline{AB}$ by a point $P$ (where $P$ is between $A$ and $B$) is the ratio of the lengths of the two segments formed,which is $\frac{AP}{PB}$.Thus,$P$ divides $\overline{AB}$ from $A$ in the ratio $\frac{AP}{PB}$.

Class 10 Mathematics Coordinate Geometry Mix Examples - Coordinate Geometry

Easy

$\overline{AB}$ is given. If $P$ is a point on $\overline{AB}$ such that $P \neq A$ and $P \neq B$,then $P$ divides $\overline{AB}$ from $A$ in the division ratio $\ldots \ldots \ldots \ldots$

A
$\frac{AP}{PB}$
B
$\frac{AP}{AB}$
C
$\frac{PB}{AP}$
D
$\frac{PB}{AB}$

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If the vertices of $\Delta LMN$ are $L(1,4), M(4,1)$ and $N(4,4),$ then $\Delta LMN$ is.......

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Show that,for every $a \in R$,the area of the triangle having the vertices $A(5, a)$,$B(2, 5)$,and $C(2, 3)$ is $3$ square units.

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Given points $A(3, 4)$ and $B(5, -2)$. Find the point $P(x, y)$ on the plane such that $PA = PB$ and the area of $\Delta PAB = 10$.

Medium

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$\overline{AB}$ is given and $P$ is a point such that $A-P-B$. If $P$ divides $\overline{AB}$ from $A$ in ratio $2:3$,then $P$ divides $\overline{AB}$ from $B$ in ratio $\dots$.

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$\overline{AB}$ is given. If $P$ is a point on $\overline{AB}$ such that $P \neq A$ and $P \neq B$,then $P$ divides $\overline{AB}$ from $A$ in the division ratio $\ldots \ldots \ldots \ldots$

Similar Questions

If the vertices of $\Delta LMN$ are $L(1,4), M(4,1)$ and $N(4,4),$ then $\Delta LMN$ is.......

Show that the centroid of the triangle with vertices $(a, b-c)$,$(b, c-a)$,and $(c, a-b)$ lies on the $X$-axis.

Show that,for every $a \in R$,the area of the triangle having the vertices $A(5, a)$,$B(2, 5)$,and $C(2, 3)$ is $3$ square units.

Given points $A(3, 4)$ and $B(5, -2)$. Find the point $P(x, y)$ on the plane such that $PA = PB$ and the area of $\Delta PAB = 10$.

$\overline{AB}$ is given and $P$ is a point such that $A-P-B$. If $P$ divides $\overline{AB}$ from $A$ in ratio $2:3$,then $P$ divides $\overline{AB}$ from $B$ in ratio $\dots$.

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